Posted by: jiunjiewang | September 24, 2012

HW1 Stats:

Mean: 54.95
Median: 62

Questions 1 and were graded by Zihe and question 3 was graded by me (Jiun-Jie). Any questions regarding the grading of a question should be directed at the appropriate TA. If there are any questions, you can come to our office hours, recitations, or email us.

There were a few common mistakes on this homework that we would like to go over.

For question 1a,a counter example is enough,you don’t need to use rules to “prove” it.
For 1b, you should formally prove it. Giving an example is far from enough.
For question 2, you should mention how to switch or rearrange in your statement. And then use an example to show how to execute yourÂ method in detail.

For question 3:

(1) most students don’t give a general instance (preference list) with multiple stable matchings.

(2) some students give a general instance partially. For example, their answer looks like as follows:
Step 1: partition n men (m_2, m_2, …, m_n) and n women (w_1, w_2, …, w_n) into n/2 groups:
(m_i,m_{i+1}, w_i, w_{i+1}), (m_i, m_{i+1}, w_i, w_{i+1}), i is odd positive number.

Step 2: assign preference list for each group by following rules:
m_i: w_i>w_{i+1}
m_{i+1}: w_{i+1}>w_i
w_i: m_{i+1}>m_i
w_{i+1}: m_i>m_{i+1}

In the above preference list, they didn’t mention that the orders of other guys, {m_1, m_2, …, m_{i-1}, m_{i+2}, m_{i+3}, …, m_n}
and {w_1, w_2, …, w_{i-1}, w_{i+2}, w_{i+3}, …, w_n}.